1. A Model with a Small and a Large Country (100 points) Let us consider a one-period model with two countries. Each of them is denoted by a subscript i E {1,2}. Country 1 is populated by 1 perfectly competitive household and by 1 perfectly competitive firm who owns K unit(s) of physical capital. Country 2 is populated by 10 perfectly competitive households and by 1 perfectly competitive firm who owns 10K unit(s) of physical capital. Each household in country i = {1,2} is endowed with T unit(s) of time that can be allocated between leisure: x; and work: li. Each unit of time allocated to work gets paid a real wage w. The preferences of household i are represented by the following logarithmic utility function: U = Olnc + Inx where c stands for the consumption of the tangible produced commodity and 0 (0,1) denotes a preference parameter. Each firm in country i produces Y; unit(s) of a tangible commodity using L unit(s) of labour and K unit(s) of physical capital according to the following Cobb-Douglas production function: 1- Y = AL K where a(0,1), A>0 are production parameters. The profit of the firm in country i denoted by II; is equally shared among the household(s) of country i who each receives a dividend income . 3) Derive expressions for the competitive labour supply of the household in country 1: 1{, the competitive labour demand: L, and the maximized profit: Max of the firm in country 1 given the wage rate w. (15 points)